Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems

[摘要] The BiconjugateA-Orthogonal Residual (BiCOR) method carried out infinite precision arithmetic by means of the biconjugateA-orthonormalizationprocedure may possibly tend to suffer from two sources of numericalinstability, known as two kinds of breakdowns, similarly to those of theBiconjugate Gradient (BCG) method. This paper naturally exploits thecomposite step strategy employed in the development of the compositestep BCG (CSBCG) method into the BiCOR method to cure one of thebreakdowns called as pivot breakdown. Analogously to the CSBCG method,the resulting interesting variant, with only a minor modification to theusual implementation of the BiCOR method, is able to avoid near pivotbreakdowns and compute all the well-defined BiCOR iterates stably on theassumption that the underlying biconjugateA-orthonormalization proceduredoes not break down. Another benefit acquired is that it seems to be aviable algorithm providing some further practically desired smoothing ofthe convergence history of the norm of the residuals, which is justifiedby numerical experiments. In addition, the exhibited method inheritsthe promising advantages of the empirically observed stability and fastconvergence rate of the BiCOR method over the BCG method so that itoutperforms the CSBCG method to some extent.

[学科分类] 应用数学